In Kelleher, Klopp has the most established academy goalkeeper to come through the ranks at Kirkby in many, many years.
But with Alisson having signed a new six-year contract with the club in August, which will take him past his 34th birthday, it is doubtful that Kelleher – who will be nearly 29 by that point – will remain content serving as his deputy.
For now, however, Klopp is adamant the Republic of Ireland international is in the best place for his long-term progress.
“For young goalkeepers, it’s about development, and Caoimhin developed here in the position incredibly well,” he told reporters.
“There’s absolutely no intention to sell him or something like that, or give him on loan, not at all. Because we need a strong No. 2.
“Would winning a trophy help [convince him to stay]? You’ll have to ask Caoimhin that.
“But he has a long-term contract here and we have a long-term plan with him.”
“Of course, we want to help the boy as well to become the best version of himself. That’s what we did so far, that’s what we will do as well.”
Despite his insistence that there is “no intention” of either selling Kelleher or sending him out on loan, Klopp appeared to soften as he discussed his prospects behind Alisson.
But the manager insisted this would be contingent on Liverpool establishing a similarly talented replacement, with 19-year-old Brazilian Marcelo Pitaluga clearly the next in line.
“Maybe there’s a time where he has to go on loan. I’m not sure if that will be next year or maybe a year later,” Klopp continued.
“Marcelo is already on a good way, really we have to judge that situation, Adrian is still here and doing an incredible job.
“We will see, but you need the quality we have here, and if we get weaker if he wants to go somewhere, then we don’t have the chance to do that.
“If we can keep the quality, then we could talk, but that’s difficult.”
Kelleher was the hero at Wembley on Sunday, keeping a clean sheet over 120 minutes before scoring the decisive penalty in an 11-10 shootout win, having caught the eye as Liverpool’s cup goalkeeper.
“He had 120 minutes,” the manager explained.
“When you asked me last week if he would play before [the final] so he could get some rhythm, I said: ‘No, he’s used to the situation where he comes on and just has to play’.
“He’s not used to 120 minutes and being the hero.
“There’s no need to stress the situation now. So no, he will not start.”